Hats & Bats is trying to decide if a new project is worth investing money into. The project would require $$273$ as initial investment. In the next $3$ years it would generate profits in the following amounts: $$82$ in year $1,$ $$113$ in year $2,$ and $$65$ in year $3.$ The typical rate of return for projects like this is $7\mathrm{.}1$ percent.

Calculate the profitability index of this proposed project.